Isotropic soft-core potentials with two characteristic length scales and anomalous behaviour

Isotropic soft-core potentials with two characteristic length scales have been used since 40 years ago to describe systems with polymorphism. In the recent years intense research is showing that these potentials also display polyamorphism and several anomalies, including structural, diffusion and density anomaly. These anomalies occur in a hierarchy that resembles the anomalies of water. However, the absence of directional bonding in these isotropic potentials makes them different from water. Other systems, such as colloidal suspensions, protein solutions or liquid metals, can be well described by this family of potentials, opening the possibility of studying the mechanism generating the polyamorphism and anomalies in these complex liquids.